Answer
Showed that given statement, $\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$,
is an identity as left side transforms into right side.
Work Step by Step
Given statement is-
$\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$
Left Side = $\sin\theta\tan\theta + \cos\theta$
= $\sin\theta\times\frac{\sin\theta}{\cos\theta} + \cos\theta$
(Using ratio identity for $\tan\theta$)
=$\frac{\sin^{2}\theta}{\cos\theta} + \cos\theta. \frac{\cos\theta}{\cos\theta} $
=$\frac{\sin^{2}\theta}{\cos\theta} + \frac{\cos^{2}\theta}{\cos\theta} $
=$\frac{\sin^{2}\theta + \cos^{2}\theta}{\cos\theta}$
=$\frac{1}{\cos\theta}$
= $\sec\theta$
= Right Side
i.e. Left Side transforms into Right Side
i.e. Given statement, $\sin\theta\tan\theta + \cos\theta$ = $\sec\theta$,
is an identity.
